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1 Intra-industry trade, environmental policies and innovations: The Porter- Hypothesis revisited Gerhard Clemenz March 2012 Abstract: According to the Porter Hypothesis (PH) stricter environmental regulations in one country may trigger innovations which may more than offset the compliance costs of domestic firms and improves their international competitiveness. In this paper it is investigated whether conditions exist under which this Hypothesis is valid either in its weak form or in its strong form where firms profits are increased. A model of intra-industry trade based on the ideal variety approach is used to identify various effects which work in favor of the PH. It is shown that the strong version may hold if environmental regulations affect consumers willingness to pay for products of green firms or if there are economies of scope in R&D which increase the probability of success of a process innovation. JEL-Classification: Q2, F1 Key Words: Intra-industry trade, R&D competition, Porter Hypothesis Address of the Author: Harvard Kennedy School Mossavar-Rahmani Center for Business & Government 79 JFK Street Cambridge, MA

2 Intra-industry trade, environmental policies and innovations: The Porter- Hypothesis revisited 1. Introduction For a long time many governments were very reluctant to impose environmental regulations in their respective countries as it was argued that this would lead to a competitive disadvantage for domestic firms as compared to foreign competitors who were not subject to similar regulations. In the early 1990s, however, the father of the concept of international competitiveness, Michael Porter, turned this argument on its head by claiming that quite the opposite of what conventional wisdom would have might happen. Strict environmental regulations do not inevitably hinder competitive advantage against foreign rivals; indeed, they often enhance it. (1991). Similarly, a few years later in the Journal of Economics Perspectives he stated Properly designed environmental regulations can trigger innovation [broadly defined] that may partially or more than fully offset the costs of complying with them in some instances (Porter & van der Linde, 1995). While the possibility that environmental regulations may trigger innovations that partially offset the cost of complying with them the Weak Porter Hypothesis was widely accepted, the Strong Porter Hypothesis that firms subject to regulations may eventually gain an advantage over their unregulated rivals and enjoy higher profits than without regulation was fiercely rejected by many economists (Palmer, K., W.E. Oates and P.R. Portney 1995). Although Porter s reasoning is quite suggestive and has appealed to many politicians, the empirical evidence in support of his Strong Hypothesis is far from convincing, and rigorous theoretical foundations are scarce. As far as empirical evidence is concerned, however, it must be emphasized that the claim 1

3 is not that the Strong Porter Hypothesis is always valid, or is valid in the majority of cases. The claim is merely that it may be valid in some instances. Consequently, there seems to be a need to identify at a theoretical level circumstances under which it is likely to be valid. The present paper attempts to help to fill this gap. From a theoretical point of view there are two lines of research that may lead to a foundation of the Porter Hypothesis. The first is based on some form of market failure, the second on organization failures inside firms, in particular the separation of management and ownership and resulting principal-agent problems. In this paper we focus on the first aspect. It is well known that environmental problems are not easily overcome in completely unregulated markets because of external effects. It is also widely accepted that R&D of private firms may be below the socially efficient level for similar reasons. Firms very often cannot appropriate the entire benefit of an innovation as some of it is usually passed on to consumers, and other firms may benefit from spillovers. The question is, however, why such inefficiencies could be overcome by stricter environmental regulations. In this paper we suggest several reasons why this may work. Our starting point is a situation in which a cost reduction is available which is greater than the costs of implementing it, but firms don t make use of it because their private benefit is smaller than the social one. We continue by assuming that in one country an emission tax is introduced which forces the firm to invest in abatement, thereby raising their marginal costs of production. If nothing else happens this raises their prices and reduces their market shares as compared to unregulated competitors in the other country. In fact, everything else equal, the cost reduction is now more profitable for the latter and we may get a complete reversal of the Porter Hypothesis. We then identify effects which work in its favor. The first is that the introduction of environmental policies may increase consumers willingness to pay for products produced with fewer emissions. Even if we impose the plausible restriction that this increase in the willingness 2

4 to pay must not exceed the value of the emission reduction, this effect may be strong enough for providing a rationale for the Strong Porter Hypothesis. The second effect that may work in this direction involves economies of scope in R&D. We consider two possibilities. The first is that abatement may require R&D investments which may also be utilized for the cost reducing process innovation. This effect may be strong enough to incentivize the regulated firms to implement the latter. It is also possible that in addition also the unregulated firms invest in cost reductions. This effect, however, supports only the Weak Porter Hypothesis. The second possibility for economies of scope in R&D to work is a reduction of risk. R&D for abatement technologies may generate additional knowledge which increases the probability of success for the cost reducing process innovations sufficiently to render it profitable. In this case the Strong Porter Hypothesis may be true from an ex post point of view. A final possibility is the availability of a technology which is superior to the one in use, both with respect to emissions as well as with respect to private costs. Since firms only care for the latter they have no incentive to switch to it, but if emission costs are internalized via an emission tax the innovation may become profitable, though only the Weak Porter Hypothesis can hold. All theoretical explanations of the Porter Hypothesis have in common that they only work for emission levels which are not too large relative to abatement costs. For the formal analysis we use a model of intra-industry trade based on the ideal variety approach as initiated by the Hotelling model of spatial competition (1929). Focusing on intraindustry trade seems to be a natural choice as we want to compare the performances of the same or similar industries in countries with different environmental policies. We prefer the ideal variety model to the more frequently used love of variety approach of monopolistic competition as the latter rules out strategic competition between firms. 3

5 The plan if the paper is as follows. In the next section we review very briefly related literature. In section 4 we sketch the Hotelling model and in section 5 we analyze R&D competition in this framework. While this may be of some interest in itself, its main purpose is to prepare the ground for analyzing the scenarios described above. We conclude with a summary of results and an outlook to future research. 2. Related Literature Since the Porter Hypothesis does not claim that environmental regulations always trigger innovations which benefit not only society as a whole but even the firms which are subject to such regulations, we take first a quick look at the empirical evidence in order to see whether this happens at least sometimes. One of the first extensive surveys of the empirical evidence was provided by Robert Stavins et al. (1994). They conclude that there is little evidence that the introduction of stricter environmental regulations in the U.S.A. has significantly reduced the international competitiveness of its industries, which could be interpreted as supporting the Weak Porter Hypothesis. On the other hand, however, they find little or no support for the Strong Porter Hypothesis. In a more recent survey Ambec et al (2010) review 17 empirical studies and find some support for the Weak Porter Hypothesis. Only two of the studies, however, can be considered as evidence in favor of the Strong Hypothesis. It is noteworthy, however, that more recent studies tend to be leaning more in the direction of the Porter Hypothesis than older ones. This may be partly due to the fact that the design of environmental regulations has been improved over the years as they have become more market based and less rigid. Secondly, the results are more supportive of the Porter Hypothesis if time lags are taken into account. This seems to suggest that innovations may indeed be triggered by environmental policies, but it takes time for them to become effective. Our conclusion is that the empirical evidence, while not 4

6 unambiguously in support of the Porter Hypothesis, suffices to make a theoretical analysis of its arguments worthwhile. There have been several attempts to provide theoretical foundations for the Porter Hypothesis despite its strong rejection on theoretical ground by Palmer et al. (1995). Broadly speaking there are two strands of literature, the first one is based on organizational failures of firms, the other on market failures. A difficulty with both types of approaches is that it is not clear why and how environmental policies can help to overcome these failures. Turning to organizational failures first, they occur mainly because of the separation of ownership and management. As a consequence decisions of a firm may not be guided by the maximization of its expected profits, but by some other objectives of managers. Managers may be more risk averse than owners who have better opportunities for risk spreading (Kennedy 1995). Managers may also be more myopic as their income depends very much on current performance and they stay at a firm only for a limited period of time (Ambec and Barla 2006). There may also be information asymmetries between owners and managers, but also between different departments inside a firm, creating various principal-agent problems (Schmutzler 2001, Ambec and Barla 2002). All these factors have the effect that profitable investments in R&D may not be made without some outside impetus, which in turn may be provided by environmental policies. The literature closer to the present paper is based on imperfect competition and market failures. Socially desirable innovations may not be made because the private returns to R&D are smaller than the social ones. One possible reason are spillovers as assumed by Mohr (2002) and Greaker (2006). If firms are forced to innovate they all profit from positive externalities and are better off than before. Andre et al (2009) show that environmental standards may help to overcome coordination failures. Simpson and Bradford (1996) use a Brander-Spencer type model of strategic trade policy to show that environmental regulation may lead to a strategic advantage of 5

7 domestic firms. The model most similar to the present one can be found in Kriechel and Ziesemer (2006). They use the Hotelling model of spatial competition to show how a tax imposed on firms who do not innovate may break an inefficient equilibrium in a waiting game of R&D competition, and they suggest that this result may be applied to environmental regulations in order to obtain a rationale for the Porter Hypothesis. 3. The ideal variety approach We focus on intra-industry trade which is driven by the desire of consumers to obtain a variety of a differentiated product which is as close as possible to their ideal variety. On the production side it is assumed that each firm produces one variety at constant marginal costs denoted as c. Each consumer buys one unit of one variety if its utility is not smaller than its price. The utility function of consumer i is defined as follows: u i (p j, a ij ) = p j a ij (1) A consumer i is characterized by the location of her ideal variety in the space of all possible varieties, which is assumed to be the unit interval. Similarly, good j is defined by its location in the varieties space, and a ij denotes the distance between the two. The price of variety j is denoted as p j, is the gross utility of the differentiated product which is the same for all varieties and all consumers, and is the constant marginal disutility of the distance between ideal and consumed variety. Consumer i is indifferent between variety j and variety k if the following indifference condition holds p j + a ij = p k + a ik (2) The original version of this model dates back to the seminal paper of Hotelling (1929) who used it for analyzing spatial competition between two firms. Each of the two firms has to choose a location in the unit interval, over which a continuum of consumers with measure one is uniformly distributed. Without price competition both firms would locate in the middle of the interval, with 6

8 price competition they locate at the opposite endpoints of the interval. 1 Subsequently various authors have changed the interpretation of this model from spatial competition to competition in terms of product characteristics (Lancaster, Salop (1979)). An extension to more than two firms and varieties has been proposed by Salop (1979) who assumed that the space of varieties is a circle. In order to keep the analysis as simple as possible we use the Hotelling version with only two firms, but at least some of our results would carry over quite easily to the more general case with more than two firms. We assume that there are two firms who are located at the endpoints of the unit interval. The indifference condition (2) can be rewritten as p 1 + x = p 2 + (1 x) (2 ) where x denotes the location of the marginal consumer, who is indifferent between the two varieties at given prices. Since consumers are uniformly distributed over the unit interval, x measures the fraction of consumers buying good 1. Consequently, we get the demand function Given the marginal costs of production, denoted as c i and c j respectively, each firm sets its price in order to maximize its profit i which is defined as i (p i, p j ) = (p i c i )(x(p i, p j ), i j, i, j = 1, 2. (4) It is well known that in equilibrium we get 1 As has been shown by this result does not hold if the disutility of the distance between ideal and consumed variety is linear in this distance. As we do not consider the choice of locations we ignore this problem. 7

9 In what follows we shall use (7) repeatedly in order to evaluate the profitability of cost reducing innovations. 4. Process innovations 4.1 Identical firms before innovations In this section we investigate the incentives to invest in process innovations in the ideal variety model. Consider first the symmetric case with c 1 = c 2 = c before an innovation. Suppose there exists another technology with marginal costs c < c which can be implemented by incurring fixed investment costs equal to z. We get a two stage game in which firms decide whether to make the cost reducing investment or to produce at costs c, and in the second stage they compete in prices as described in section 3. We get the following payoff matrix. Firm 2 Y N Firm 1 Y /2 z, /2 z 1 (c, c) z, 2 (c, c) N 1 (c, c), 2 (c, c) z /2, /2 From (7) it follows that Consequently, no innovation by either firm is the unique Nash-equilibrium in pure strategies if Note that this is compatible with z < [c c]/2, requiring 3 > c c, hence the innovation would be beneficial from a social point of view, though it is not from the point of view of firms. 8

10 Using again (7) we get Consequently, innovation by each firm is the unique Nash-equilibrium in pure strategies if Finally, we get an asymmetric equilibrium with only one firm innovating if As noted above both firms should innovate from a social point of view if z < [c c]/2 which is compatible with (8) implying that no firm innovates, but also with condition (10) which leads to an asymmetric equilibrium. The reason for that inefficiency is that an innovating firm appropriates only a fraction of the social gain as it will pass on part of the cost reduction to consumers. In the next section we investigate the innovation game for c 1 > c 2 before innovation takes place. 4.2 Asymmetric firms before innovation The basic claim of the Porter-Hypothesis is that putting pressure on the profits of the domestic firm via stricter environmental regulations may lead to R&D-investments which would not take place otherwise. The simplest way to model this in the present framework is to assume that only one firm, say firm 1, faces higher marginal costs than the other one, hence c 1 > c 2 = c. One interpretation for this is that the production of one unit of output causes emissions which in turn inflict damage on the economy that equal e in monetary terms. This externality can be internalized by imposing an emission tax. For = 1 and no abatement we get c 1 = c + e. We shall return to this and alternative interpretations of the cost difference imposed by government policies later and look first at its implications for the R&D-game. We shall distinguish two cases. 9

11 In the first case the innovation reduces the marginal costs of production by a fixed amount denoted as ρ, in the second case the marginal costs of production are c regardless of the initial level of unit costs. In line with our interpretation of cost increases due to the internalization of emission costs the first case would correspond to a new technology with the same emissions as before and smaller private marginal costs, whereas in the second case we would have a superior green technology with no emissions and smaller private marginal costs Identical absolute cost reductions We assume that hence at the outset the cost reduction is socially desirable but not profitable from the firms point of view. Note that (11) requires 3 > c c (11 ) In this section it is assumed that the innovation reduces marginal costs by ρ = c c. Consider next a government policy that increases the costs of firms 1 from c to c 1 > c. Both firms have still the option to reduce their marginal costs by ρ. Using (7) we get the following profits excluding R&D-cost z depending on whether the innovation is implemented by none, one or both firms: 10

13 The intuition behind this result is the following. The innovation implies that unit costs of production go down, and the benefit for the firm is increasing in the volume of its output. An implication of this result is that the Nash-equilibrium with no innovation by either firm will be broken if the marginal costs of firm 1 are increased sufficiently. Proposition 2: Suppose inequality (11) holds. There exists c 1 > c such that the inequality is reversed and firm 2 implements the cost reducing innovation. Proof: Note that ρ = c c. Combining (11) and (19) yields which holds for c 1 sufficiently large. Q.E.D. As far as the Porter-hypothesis is concerned this result is its reversal as the firm facing the less restrictive (or no) regulation has the greater incentive to innovate. We shall look at welfare implications, in particular with respect to environmental concerns, in section 5. Now we turn to the second possibility, a reduction of marginal costs to c regardless of current costs including taxes and/or costs of abatement Identical achievable marginal costs If neither firm innovates profits are given by (12) and (13), if both firms innovate profits are /2, excluding R&D costs. If only firm 2 innovates profits are given by (16) and (17), replacing c ρ by c. If only firm 1 innovates we get the following gross profits. 12

14 The payoff matrix of the R&D-game is therefore Firm 2 Y N Firm 1 Y /2 z, /2 z 1 (c, c) z, 2 (c, c) N 1 (c 1, c), 2 (c 1, c) z 1 (c 1, c), 2 (c 1, c) We show next that an innovation that allows switching to the alternative technology with marginal costs c may be more profitable for firm 1. Proposition 3: Let c 1 > c 2 = c. The implementation of a new technology with marginal costs c < c is more profitable for firm 1 if and only if 3 + c [c 1 +c]/2. Proof: Subtracting (12) from (21) yields Recall (19), the corresponding return if only firm 2 innovates. Subtracting (19) from (23) yields The intuition behind this result is as follows. Firm 2 has the advantage that its output is greater than that of firm 1 before the switch of technologies, hence the cost reduction is more profitable. However, this difference in output is decreasing in which can be interpreted as a measure of the monopoly power of the two firms. On the other hand, the relative cost reduction is smaller for firm 2 the closer c is to c. 13

15 The important implication for our purpose is the possibility that imposing an emission tax on firm 1 may induce it to switch to the superior technology with marginal costs c while firm 2sticks to the old technology. For the record we state this as a proposition. Proposition 4: There exist values for the parameters, c 1, c and c with c 1 > c > c, such that the following inequalities hold Proof: follows from Propositions 2 and 3. Q.E.D. Thus we have set the stage for analyzing the impact of environmental policy measures on R&D and innovations which are implemented by one country, but not by its trading partner. 14

16 5. Emission Tax and Welfare Effects In section 4 it was left open where the difference in the marginal costs of two firms engaged in (potential) R&D competition comes from. In the remainder of the paper we shall assume that the two firms are located in different countries and one of them is subject to environmental policies which increase its costs of production before a process innovation takes place. Without loss of generality we assume that only country 1 implements such measures, thus increasing the costs of firm 1. Regardless of where production takes place there is an emission per unit of output which causes damage. The monetary value of this damage is denoted as e. 2 Note that this implies a uniformly mixing pollutant like greenhouse gases which do the same damage regardless of where they originate from. Denote the emission tax per unit of the pollutant as. If emissions are not reduced the costs per unit of output of firm 1 are increased by e, hence c 1 = c + e. If no emission reduction is feasible then in view of Propositions1 and 2 an emission tax is a non-starter as it reduces domestic production without affecting overall emissions. To see this more clearly and for later reference it is useful to define a welfare function for country The Domestic Welfare Function Domestic welfare is defined as total utility enjoyed by domestic consumers minus total costs. Costs include the costs of production, environmental costs including abatement costs, and net expenditures on imports, i.e. the value of exports minus the value of imports. Domestic population equals 1/2, hence aggregate consumer utility equals [ [x x 2 2 ]/2]/2. The second expression inside the squared brackets captures the average disutility of consumers not getting 2 For the sake of simplicity we assume that emissions are measured in units such that e also denotes the physical quantity of the pollutant. 15

17 their ideal variety. Denoting the aggregate value of this disutility for country 1 as D 1 and substituting for x 1 and x 2 we get Turning to total costs in country 1 without emission tax we get e + cx 1. If an emission tax is introduced the change in the costs of production depends on the availability of an abatement technology and its properties. If no abatement is technically possible the tax will simply increase the marginal costs of firm 1 and shift production to country 2. Total emissions remain the same, country 1 has lower production costs but incurs a balance of trade deficit as it imports more of variety 2 than it exports of its own variety (see below). As in this situation an emission tax is ineffective we shall assume that abatement is possible via an end-of-pipe technology. Emissions per unit of output can be reduced by an amount r, but marginal costs of production will be increased according to the strictly convex and increasing function k(r). For the sake of tractability we shall assume k(r) = r 2 /2. For a given emission rate e and the emission tax rate firm 1 will choose r in order to minimize the total increase in its marginal costs, hence it solves min[c 1 c] = [e r] + k(r) = [e r] + r 2 /2, (25) where c 1 denotes the marginal costs of firm 1 after the introduction of the emission tax. The solution of (25) is r =. (26) Substituting (26) in (25) yields c 1 c = min{e 2 /2, [e /2]}. (27) For a given output x 1 total emission costs in country 1 are E 1 ( ) = e [ 2 /2]x 1 (28) 16

18 For x 1 fixed the optimum tax rate * equals * = min{e, 1}. (29) In fact, since r e the tax rate = 1 would achieve the optimal emission reduction also for e < 1. Furthermore, since the marginal damage of emissions equals 1 this tax rate satisfies the property that marginal cost of emission equals the marginal emission tax rate. However, in the open economy x 1 will be affected by, and so will D 1 and the balance of trade, denoted as B 1, which we consider next. As country 1 exports half of its own output and imports half of the output of country 2 the balance of trade of country 1 is defined as follows. B 1 = [p 1 x 1 p 2 x 2 ]/2. Substituting for prices and quantities the expressions given in (5) and (6) we get after some simplifications Collecting terms domestic welfare as a function of c 1 and c 2 is defined as follows. We show first under which condition a strictly positive emission tax in country 1 increases its domestic welfare. Proposition 5: There exists a strictly positive emission tax rate which improves the domestic welfare of country 1as compared to the welfare level without tax if e < 6 + 2c/. Proof: Substituting (27) for c 1 c in (30) and differentiating with respect to yields for = 0 which is greater than 0 if e < 6 + 2c/. Q.E.D. 17

19 Introducing a (small) emission tax has three effects on domestic welfare: It incentivizes the domestic firm to reduce its emissions. At the same time domestic prices go up and the trade balance deteriorates. Finally, since production of the differentiated product is reduced the costs of production are reduced as well. Note that the way welfare is defined implies that tax revenues which occur only if abatement is not complete are used in a way that does not affect domestic welfare, and price changes affect only the distribution of income between the domestic firm and the domestic consumers. Proposition 5 states that a welfare improving emission tax exists, but leaves open what the optimal tax rate actually is. As we have shown elsewhere (Clemenz 2012) the optimal tax rate will induce full abatement if e < 1 and is sufficiently large. Since in this paper we are not concerned with determining the optimal tax rate but rather with its power to trigger off innovations which benefit the domestic economy as a whole, and even the firm which is subject to the tax, but would not be undertaken without it, we confine attention to values of e < 1 with large enough to make =1 and full abatement the optimal choices. 18

20 6. Incentives for Cost Reductions In this section we assume that the abatement technology and the reduction of the private production costs of the firm are separated, i.e. abatement costs r 2 /2 are added to the private costs of production which are equal to c if no further innovations are implemented. By spending an amount z these private costs of production can be reduced to c. According to proposition 1 such a cost reducing innovation is more profitable for firm 2 which is not forced to pay emission taxes and/or reduce emissions, and in fact if total marginal costs of firm 1 are sufficiently increased by the environmental policies of its country firm 2 may implement the innovation, contrary to what the Porter Hypothesis would suggest. While according to Proposition 5 a welfare increasing emission tax still exists for country 1, it may be smaller than without the threat of an innovation in country 2 which would shift the production of the differentiated product even more to firm 2, thus counteracting the beneficial effect of the emission tax. We shall not pursue this question any further, however, but consider factors that may work in favor of R&D investments of firm 1 in line with the Porter Hypothesis. 6.1 Changed Willingness to Pay The introduction of stricter environmental policies may lead to an increased awareness of consumers reflected in a greater willingness to pay for goods which are produced with less pollution, thus conferring a competitive advantage to the firm with the cleaner production process. While it is conceivable that this effect could also be achieved by a campaign of a firm aimed at convincing consumers to prefer products which are produced in a more environment friendly way, there are plausible arguments why a firm would hesitate to try such an approach. Probably most importantly, such a campaign would be costly, thus adding to total expenditures for reducing emissions and overall costs of production. Secondly, the government may be more 19

21 credible than a firm when advocating and forcing the implementation of cleaner production processes. The question remains, of course, whether the increase in the willingness to pay for products of a green firm would be large enough to make up for the additional abatement costs, and even induce further cost reducing innovations. Within our basic framework we assume that only the consumers in country 1are willing to pay more for products of a green firm, formally this is captured by an increase of in the utility function of consumers in country 1. It seems reasonable to assume that only consumers in that country which implements environmental policies change their preferences, or at least they do so to a larger extent than consumers in the other country. We also assume that the law of one price still rules, i.e. the firms cannot charge different prices for their product in different countries. Both assumptions make it less likely that a green firm benefits from its increased abatement efforts with respect to consumer demands in comparison to the alternatives of higher willingness to pay in both countries, or price discrimination between the two countries. Turning to the formal analysis the main change concerns the utility function of consumers in country 1. Instead of (1) we get u i (p 1, a i1 ) = p 1 a i1 (32a) for a consumer in country 1 buying good 1, and u i (p 2, a ij ) = p 2 a i2 (32b) if the same consumer buys good 2. Note that 1 >. Consequently, instead of (2) the indifference condition for the consumers in country 1 now reads p 1 + a i1 = p 2 + a i2 + 1 (33) 20

22 Define Δ := 1 Note that in country 2 indifference condition (2) continues to hold. Adding the resulting demand functions for the two firms in each country they maximize their respective profit functions, setting prices in a non-cooperative way. The corresponding first order conditions are 2p 1 + p c 1 + Δ = 0 2p 2 + p c 2 Δ = 0 (35a) (35b) Solving for prices and quantities yields A comparison of (37a) and (37b) shows that firm 1 sells a larger quantity than firm 2 if Δ > 2(c 1 c 2 ). If this condition holds a cost reduction is more profitable for firm 1 than for firm 2, and we can state Proposition 6: A reduction of the constant marginal costs of production increases profits of firm 1 by a larger amount than profits of firm 2 iff Δ > 2(c 1 c 2 ). Proof: Substituting (36a) (37b) in the profit equation (34a) and (34b) yields 21

23 Differentiating profits with respect to costs yields and clearly, 1 / c 1 < 2 / c 2 iff Δ > 2(c 1 c 2 ). Q.E.D. The question arises, of course, whether the condition given in Proposition 6 can reasonably be assumed to hold within the framework of our model. In particular, Δ cannot be arbitrarily large if consumers are rational. We assume that the willingness to pay for the variant produced by a green firm cannot exceed the difference in the emissions per unit of output, hence Δ r =. (40) Suppose (40) holds as an equality. We show next that Δ > 2(c 1 c 2 ) can only hold for e 1. Proposition 7: Suppose Δ = r and k(r) = r 2 /2. Δ > 2(c 1 c 2 ) iff e 1. Proof: Recall that according to (27) c 1 c = min{e 2 /2, [e /2]}. Suppose first r = e. Clearly, e 2 /2 e/2 requires e 1. For < e we get [e /2] /2 or 2e 1 which contradicts e > 1 and < e. Q.E.D. Economically this simple result has the following interpretation. Even if consumers are willing to pay more for the product of a green firm, imposing an emission tax will only provide an 22

24 increased incentive for cost reducing innovations if emissions are not too large relative to abatement costs. On the other hand, for e < 1 an emission tax may provide incentives for innovations even if the willingness to pay of domestic consumers is smaller than the reduction of emissions. As we have shown elsewhere (Clemenz 2010), if domestic consumers differ with respect to their valuation of abatement then their average willingness to pay matters, hence for e sufficiently small the condition of Proposition 6 will still be satisfied. In view of Propositions 6 and 7 the following scenario is possible: Without an emission tax no firm is willing to carry the costs of implementing a cost reducing innovation as condition (8) holds. After the government introduces an emission tax in country1, marginal costs go up for firm 1 which increases the incentive for firm 2 to innovate. If emissions per unit of output are small relative to abatement costs, and the willingness to pay for the product of the now green firm 1 is increased sufficiently in country 1, however, this innovation may be more profitable for firm 1 than for firm 2. Of course, it is conceivable that still neither firm wants to innovate, or both, or only firm 1. The latter possibility is the one that conforms to the Porter-hypothesis in the sense that stricter environmental policies in one country stimulate innovations in this country beyond the reduction of emissions. The next proposition shows that the Porter-hypothesis may also hold in its strong version stating that the regulated firm is better off than without regulation. Proposition 8: Suppose marginal cost can be reduced by ρ through an investment z, but condition (8) holds. Suppose further that after the introduction of an emission tax in country 1 the willingness of the consumers of country 1 to pay for the product of firm 1 increases by r. There exist strictly positive values for the parameters c, e, ρ and z such that the profit of firm 1, after it has been subjected to an emission tax and invested in abatement and cost reduction, is greater than without emission tax. Proof: Recall that the equilibrium profit of firm 1 without any policy measures is /2. Suppose 23

25 e < 1 and = e = r. Substituting c 2 = c, c 1 = c + e 2 /2 ρ and Δ = e in the profit function (38a) yields Recall (7 ) which shows the profit of firm 1 of investing z without emission tax and abatement Clearly, there exist values of ρ, e and z for which the following inequalities hold 1 (c ρ, e, c) > /2 > 1 (c ρ, c) Q.E.D. Note that the second inequality is condition (8). 6.2 Economies of Scope in R&D Shared Fixed Costs It is well known that R&D requires a fair amount of fixed costs by setting up labs, hiring scientists, etc. So far we have not specified what the costs of a process innovation are, but it seems reasonable to assume that at least part of z, the required investment to reduce marginal costs by ρ, is a fixed cost. Now suppose that reducing emissions in reaction to environmental policies also requires fixed costs. It seems plausible that at least part of these fixed R&D investments can also be made available for reducing costs, thus reducing z and making the initial process innovation more profitable, in other words there exist economies of scope. In this section we investigate whether plausible conditions exist such that a reduction of z due to R&D efforts for reducing emissions can be sufficiently large to trigger off innovations which would not be implemented without forcing firms to invest in abatement in the first place. In particular, we 24

26 require two conditions to be satisfied. Fixed costs of abatement must not exceed its benefits for the firm, and the reduction of z must not exceed the fixed costs spent on abatement. Turning to the first condition first we compare the gross profits of the firm with and without abatement after the introduction of an emission tax. Fixed costs of abatement cannot exceed this difference since otherwise the firm would prefer to pay the emission tax without abatement Fixed Costs of Abatement We assume that abatement does not only increase marginal costs by an amount equal to r 2 /2, but also requires R&D expenditures, denoted as z a. Clearly, firm 1 will only invest z a if this is fully covered by an increase of gross profits due to emission reductions and reduced tax payments. Recall that according to (23) firm 1 will choose r = min{e, }, and variable emission costs per unit of output are minimized at = 1. Since our main interest is in finding conditions under which the Porter Hypothesis holds we focus on the case with e 1, implying that the government of country 1 sets = 1 and firm 1 reduces emissions to zero if z a is sufficiently small. Comparing the profits of firm 1 with and without abatement (and firm 2 producing at marginal costs c) we get (41) and (42) are obtained by substituting e 2 /2 and e for c 1 c 2 respectively in (7). Subtracting (42) from (41) yields the upper limit for the fixed costs z a firm 1 is willing to spend for abatement, hence 25

27 Note that the right hand side of (43) is only positive for e < 2. In addition, must not be too small relative to e in order to ensure that strictly positive fixed costs of abatement can be covered. More precisely, (43) can be rewritten as The expression in square brackets is positive if In what follows we assume (45) to hold Reducing Emissions and Marginal Costs Suppose that (45) holds and firm 1 has invested in abatement, thus raising its marginal costs by an amount of e 2 /2. The two firms play now the asymmetric R&D game explained in subsection with an important modification: The costs of the cost reduction for firm 1 are z 1 instead of z with z z a z 1 < z. For c 1 we get c + e 2 /2. We get the following payoff matrix for the R&D game. Firm 2 Y N Firm 1 Y 1 (c 1 ρ, c ρ) z 1, 2 (c 1 ρ, c-ρ) z 1 (c 1 ρ, c) z 1, 2 (c 1 ρ, c) N 1 (c 1, c ρ), 2 (c 1, c ρ) z 1 (c 1, c), 2 (c 1, c) Since we are interested in conditions under which some version of the Porter-Hypothesis is valid we assume that condition (8) holds. Depending on e, ρ, z and z 1 the following Nash-equilibria in pure strategies are possible: No firm reduces its costs, only one firm does it, both firms reduce their marginal costs. We derive next necessary conditions for each of these equilibrium 26

28 configurations and illustrate then our results by means of a simple numerical example. As a first step we have a look at the profits of each firm in each cell of the above payoff matrix. Note that i (c 1 ρ, c ρ) = i (c 1, c), i = 1,2. The introduction of the emission tax = 1 in country 1 does not trigger off any process innovations if the following two inequalities hold. Condition (46) states that firm 1 will not innovate if the reduction of R&D costs is too small to overcome the disadvantage of higher marginal costs which are due to abatement. Condition (47) implies that the increase of output of firm 2 made possible by its lower marginal costs is not sufficient to make further cost reductions profitable. Note that (47) requires 3 > ρ + e 2 which is slightly more restrictive than the requirement without abatement costs for firm 1. Only one firm would invest in cost reduction if only one of the above inequalities is reversed whereas the other continues to hold. According to the Porter-Hypothesis it should be firm 1. 27

29 Taking into account (43) and the restriction z 1 z z a the conditions for the existence of a Nashequilbrium in which only firm 1 invests in cost reductions are Subtracting (47) from (46a) and rearranging yields (48) is a necessary, though not sufficient condition for the existence of a Nash-equilibrium in which only firm 1 invests in a process innovation as suggested by the Porter Hypothesis. A sufficient condition for (48) to hold is e( ρ) 6 (49) Note that (49) only ensures that the necessary condition can be met, not the existence of the considered Nash-equilibrium itself. Furthermore, (47) implies (8), but not the other way round. Clearly, it is straightforward to find values for z and z 1 such that (46a) and (47) are reversed, implying a reversal of the Porter-Hypothesis. In this case it does not matter whether firm 1 reduces its emissions or pays the emission tax, firm 2 will have the double benefit of a competitor with increased marginal costs of production and a profitable reduction of its own marginal costs. In such a situation country 1 should introduce only a small tax or no tax at all, ensuring that firm 2 has no incentive to reduce costs. Similarly, it is possible to find values of z and z 1 which make R&D profitable for each firm as long as the other one sticks to its current technology, implying that the Nash equilibrium is not unique. It is less obvious that a Nash-equilibrium may exist in which both firms invest in cost 28

30 reduction as a response to environmental regulation in country 1. For this to be the case the following two inequalities have to be satisfied. The left hand side of (51) is the increase of the profit of firm 2 if it matches the cost reduction ρ of firm 1. In this case it cannot be an equilibrium that only firm 1 becomes active after the introduction of an emission tax. To see whether (51) can be compatible with (8) subtract the latter from the former. If both inequalities are to hold we must have Condition (52) states that firm 2 will find it profitable to follow up a cost reducing innovation of firm 1 after the introduction of an emission tax in country 1 if the emission level, and therefore the increase of the marginal costs of firm 1, are large relative to the feasible cost reduction. More precisely, the increase of the marginal costs of firm1 because of abatement must exceed the feasible cost reduction ρ, otherwise firm 2 would have a smaller output than without the emission tax and a cost reduction would be less profitable. In order to see whether firm 1 would also find it profitable to reduce its marginal costs even if firm 2 has already done so, we rewrite first (50) in order to include the restrictions on z a and z 1 respectively. Subtracting inequality (8) from (50a) yields the following necessary condition for the existence of a Nash-equilibrium in which both firms invest in cost reduction after the implementation of an emission tax in country 1, even if neither would have done so without tax. 29

31 Condition (53) is obviously satisfied for sufficiently large and is compatible with condition (52), hence both necessary conditions for the existence of a Nash equilibrium with both firms innovating after the introductions of environmental regulations in country 1 can be satisfied simultaneously. The existence of economies of scope in R&D may therefore lead to the positive effects of appropriate environmental policies envisaged in the Porter-Hypothesis. Before we illustrate the results of this section by presenting a simple numerical example we show, however, that only the Weak Porter Hypothesis gets theoretical support. Using (14a) the Strong Porter Hypothesis implies But this contradicts the assumptions z z a + z 1 and A Numerical Example Consider the following numerical example with =2, e = 1 and ρ = 3/8. Note that all assumptions made in the previous section are satisfied and all necessary conditions derived for the various equilibrium configurations are met. We derive first the interval of values for z for which (8) holds. Substituting the above values for and ρ in (8) yields Next we compute the upper limit for z a. Substituting 1 for e in (43) yields z a 21/

32 By varying z and z 1, while taking account of the restrictions on both, we can now generate all equilibrium configurations. Consider first the incentive to innovate for firm 1 if firm 2 sticks to its old technology. According to (43) firm 1 innovates if 33/256 3/288 > z 1, and obviously, given the admissible ranges of z and z a we can choose values for z 1 such that this inequality holds (or does not, depending on which equilibrium we want to get). Turning to firm 2, it will innovate if firm 1 does not if 33/ /288 > z, which holds for values of z close to its lower limit 33/256, but not for z close to its upper limit. Note that z a can be sufficiently large to generate values of z 1 such that firm 1 innovates while firm 2 does not. Finally, both firms innovate if 31/256 3/288 > z 1 and 31/ /288 > z. Note that the first condition is compatible with relatively large values of z whereas the second can only hold for z close to its lower limit 33/256. In any case, if it is possible that some of the fixed costs incurred for R&D in abatement and in the reduction of private marginal costs can be shared then the Weak Porter Hypothesis can hold Reducing Risk So far we have assumed that innovations do not involve any risk. Suppose next that R&D for a process innovation reducing marginal costs by ρ succeeds only with probability ω < 1. We assume now instead of (8) Before the introduction of an emission tax in country 1 no firm would innovate because of the risk, although at least one of them would if the cost reduction could be achieved with certainty as 31

33 in the case of a successful innovation the increase of the profit is greater than the expnditures for R&D. Suppose again that country 1 charges a tax per unit of emission equal to 1, e 1 and firm 1 has now to incur marginal costs equal to c + e 2 /2. Suppose in the process of implementing an abatement technology firm 1 acquires additional knowledge that increases the success probability of R&D in cost reduction drastically, for the sake of simplicity say to one. It will innovate if Subtracting the right hand side of (8a) yields or Firm 2 would not innovate alone if Subtracting this from the left hand side of (8a) yields after some rearrangements and it is straightforward to see that (54a) implies (56). In other words, if ω is sufficiently small for satisfying the necessary condition that investing in abatement makes also R&D in cost reduction profitable, then the necessary condition for firm 2 not to invest is satisfied a fortiori. This does not rule out, of course, that (46b) and the reverse of inequality (55) hold simultaneously, but the important point here is that the Strong Porter Hypothesis may hold: As a consequence of an emission tax in country 1 only firm 1 goes ahead with a cost reducing innovation and enjoys a profit increase which exceeds its R&D expenditures. Note that this 32

34 observation could also be made if both firms try to innovate but firm 2 fails, which happens with probability 1 ω. 7. Adoption of a Superior Green Technology For the sake of completeness we consider now a situation in which a superior technology with fewer emissions and smaller private costs of production is available. Since firms care only for the latter this technology may not be adopted if the reduction of the private costs of production is too small compared to the costs of adoption z. An emission tax in country 1 leads to an internalization of the costs of emissions and can thus make the adoption of the green technology profitable for firm 1. As this possibility has already been shown in Proposition 4 we need not further elaborate it here. It has to be pointed out, however, that only the Weak Porter Hypothesis can be supported by this version of our model. 8. Concluding Remarks We have shown that the Porter Hypothesis may hold, if the implementation of environmental policies leads to a change in consumer behavior, or if it induces R&D of the regulated firms who may subsequently be able to exploit economies of scope. It must be said, however, that even if such effects exist the outcome suggested by the Porter Hypothesis is by no means guaranteed, and in fact exactly the opposite may happen. In addition, the Strong Porter Hypothesis is clearly less likely to occur than its weak version. On the other hand, however, the effects analyzed are not mutually exclusive and may occur simultaneously, all pulling in the same direction and making the Porter Hypothesis more plausible. The basic model of this paper would also allow for an analysis of other effects which may support the Porter Hypothesis, in particular managerial discretion. Managers may not undertake profitable R&D projects because their personal objective function is not profit maximization, and 33

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